LAMP: A Locally Adapting Matching Pursuit Framework for Group Sparse Signatures in Ultra-Wide Band Radar Imaging

Abstract: It has been found that radar returns of extended targets are not only sparse but also exhibit a tendency to cluster into randomly located, variable sized groups. However, the standard techniques of Compressive Sensing as applied in radar imaging hardly considers the clustering tendency into account while reconstructing the image from the compressed measurements. If the group sparsity is taken into account, it is intuitive that one might obtain better results both in terms of accuracy and time complexity as compared to the conventional recovery techniques like Orthogonal Matching Pursuit (OMP). In order to remedy this, techniques like Block OMP have been used in the existing literature. An alternate approach is via reconstructing the signal by transforming into the Hough Transform Domain where they become point-wise sparse. However, these techniques essentially assume specific size and structure of the groups and are not always effective if the exact characteristics of the groups are not known, prior to reconstruction. In this manuscript, a novel framework that we call locally adapting matching pursuit (LAMP) have been proposed for efficient reconstruction of group sparse signals from compressed measurements without assuming any specific size, location, or structure of the groups. The recovery guarantee of the LAMP and its superiority compared to the existing algorithms has been established with respect to accuracy, time complexity and flexibility in group size. LAMP has been successfully used on a real-world, experimental data set.